Haasdonk, Bernard; Kleikamp, Hendrik; Ohlberger, Mario; Schindler, Felix; Wenzel, Tizian A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs. (English) Zbl 1516.65087 SIAM J. Sci. Comput. 45, No. 3, A1039-A1065 (2023). MSC: 65M60 65M06 65N30 68T07 68Q32 65C05 49M41 PDFBibTeX XMLCite \textit{B. Haasdonk} et al., SIAM J. Sci. Comput. 45, No. 3, A1039--A1065 (2023; Zbl 1516.65087) Full Text: DOI arXiv
Keil, Tim; Ohlberger, Mario; Schindler, Felix Adaptive Localized Reduced Basis Methods for Large Scale Parameterized Systems. arXiv:2303.03074 Preprint, arXiv:2303.03074 [math.NA] (2023). BibTeX Cite \textit{T. Keil} et al., ``Adaptive Localized Reduced Basis Methods for Large Scale Parameterized Systems'', Preprint, arXiv:2303.03074 [math.NA] (2023) Full Text: arXiv OA License
Wenzel, Tizian; Haasdonk, Bernard; Kleikamp, Hendrik; Ohlberger, Mario; Schindler, Felix Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling. arXiv:2302.14526 Preprint, arXiv:2302.14526 [math.NA] (2023). BibTeX Cite \textit{T. Wenzel} et al., ``Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling'', Preprint, arXiv:2302.14526 [math.NA] (2023) Full Text: arXiv OA License
Banholzer, Stefan; Keil, Tim; Ohlberger, Mario; Mechelli, Luca; Schindler, Felix; Volkwein, Stefan An adaptive projected Newton non-conforming dual approach for trust-region reduced basis approximation of PDE-constrained parameter optimization. (English) Zbl 1510.90268 Pure Appl. Funct. Anal. 7, No. 5, 1561-1596 (2022). MSC: 90C31 35J20 65N30 90C06 PDFBibTeX XMLCite \textit{S. Banholzer} et al., Pure Appl. Funct. Anal. 7, No. 5, 1561--1596 (2022; Zbl 1510.90268) Full Text: arXiv Link
Gavrilenko, Pavel; Haasdonk, Bernard; Iliev, Oleg; Ohlberger, Mario; Schindler, Felix; Toktaliev, Pavel; Wenzel, Tizian; Youssef, Maha A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows. (English) Zbl 1501.76062 Lirkov, Ivan (ed.) et al., Large-scale scientific computing. 13th international conference, LSSC 2021, Sozopol, Bulgaria, June 7–11, 2021. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 13127, 378-386 (2022). MSC: 76M99 76V05 68T05 PDFBibTeX XMLCite \textit{P. Gavrilenko} et al., Lect. Notes Comput. Sci. 13127, 378--386 (2022; Zbl 1501.76062) Full Text: DOI arXiv
Keil, Tim; Mechelli, Luca; Ohlberger, Mario; Schindler, Felix; Volkwein, Stefan A non-conforming dual approach for adaptive trust-region reduced basis approximation of PDE-constrained parameter optimization. (English) Zbl 1527.90221 ESAIM, Math. Model. Numer. Anal. 55, No. 3, 1239-1269 (2021). MSC: 90C30 35J20 65N30 90C06 PDFBibTeX XMLCite \textit{T. Keil} et al., ESAIM, Math. Model. Numer. Anal. 55, No. 3, 1239--1269 (2021; Zbl 1527.90221) Full Text: DOI arXiv
Buhr, Andreas; Iapichino, Laura; Ohlberger, Mario; Rave, Stephan; Schindler, Felix; Smetana, Kathrin Localized model reduction for parameterized problems. (English) Zbl 1523.65091 Benner, Peter (ed.) et al., Model order reduction. Volume 2: Snapshot-based methods and algorithms. Berlin: De Gruyter. 245-305 (2021). MSC: 65N30 65N55 65N15 35J20 35J25 65Y15 PDFBibTeX XMLCite \textit{A. Buhr} et al., in: Model order reduction. Volume 2: Snapshot-based methods and algorithms. Berlin: De Gruyter. 245--305 (2021; Zbl 1523.65091) Full Text: DOI arXiv
Haasdonk, Bernard; Ohlberger, Mario; Schindler, Felix An adaptive model hierarchy for data-augmented training of kernel models for reactive flow. arXiv:2110.12388 Preprint, arXiv:2110.12388 [math.NA] (2021). BibTeX Cite \textit{B. Haasdonk} et al., ``An adaptive model hierarchy for data-augmented training of kernel models for reactive flow'', Preprint, arXiv:2110.12388 [math.NA] (2021) Full Text: arXiv OA License
Ohlberger, Mario; Schaefer, Michael; Schindler, Felix Localized model reduction in PDE constrained optimization. (English) Zbl 1407.49030 Schulz, Volker (ed.) et al., Shape optimization, homogenization and optimal control. DFG-AIMS workshop held at the AIMS Center Sénégal, Mbour, Sénégal, March 13–16, 2017. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 169, 143-163 (2018). MSC: 49K20 65K10 65N30 49N20 93A15 PDFBibTeX XMLCite \textit{M. Ohlberger} et al., ISNM, Int. Ser. Numer. Math. 169, 143--163 (2018; Zbl 1407.49030) Full Text: DOI
Ohlberger, Mario; Rave, Stephan; Schindler, Felix True error control for the localized reduced basis method for parabolic problems. (English) Zbl 1448.65170 Benner, Peter (ed.) et al., Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Cham: Springer. MS&A, Model. Simul. Appl. 17, 169-182 (2017). MSC: 65M60 65M15 65M50 65M06 65J08 PDFBibTeX XMLCite \textit{M. Ohlberger} et al., MS\&A, Model. Simul. Appl. 17, 169--182 (2017; Zbl 1448.65170) Full Text: DOI arXiv
Ohlberger, Mario; Schindler, Felix Non-conforming localized model reduction with online enrichment: towards optimal complexity in PDE constrained optimization. (English) Zbl 1365.65174 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 357-365 (2017). MSC: 65K10 35Q93 65N30 PDFBibTeX XMLCite \textit{M. Ohlberger} and \textit{F. Schindler}, Springer Proc. Math. Stat. 200, 357--365 (2017; Zbl 1365.65174) Full Text: DOI
Ohlberger, Mario; Rave, Stephan; Schindler, Felix Model reduction for multiscale lithium-ion battery simulation. (English) Zbl 1355.78031 Karasözen, Bülent (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2015. Selected papers based on the presentations at the European conference, Ankara, Turkey, September 14–18, 2015. Cham: Springer (ISBN 978-3-319-39927-0/hbk; 978-3-319-39929-4/ebook). Lecture Notes in Computational Science and Engineering 112, 317-331 (2016). MSC: 78A57 78M34 78M12 35K57 80A20 78M20 PDFBibTeX XMLCite \textit{M. Ohlberger} et al., Lect. Notes Comput. Sci. Eng. 112, 317--331 (2016; Zbl 1355.78031) Full Text: DOI arXiv
Ohlberger, M.; Schindler, F. Error control for the localized reduced basis multiscale method with adaptive on-line enrichment. (English) Zbl 1329.65255 SIAM J. Sci. Comput. 37, No. 6, A2865-A2895 (2015). MSC: 65N15 65N55 65N30 65Y20 35J20 PDFBibTeX XMLCite \textit{M. Ohlberger} and \textit{F. Schindler}, SIAM J. Sci. Comput. 37, No. 6, A2865--A2895 (2015; Zbl 1329.65255) Full Text: DOI arXiv
Ohlberger, Mario; Schindler, Felix A-posteriori error estimates for the localized reduced basis multi-scale method. (English) Zbl 1305.65220 Fuhrmann, Jürgen (ed.) et al., Finite volumes for complex applications VII – methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, Germany, June 15–20, 2014. Vol. I. Cham: Springer (ISBN 978-3-319-05683-8/hbk; 978-3-319-05684-5/ebook; 978-3-319-06402-4/set). Springer Proceedings in Mathematics & Statistics 77, 421-429 (2014). MSC: 65N15 PDFBibTeX XMLCite \textit{M. Ohlberger} and \textit{F. Schindler}, Springer Proc. Math. Stat. 77, 421--429 (2014; Zbl 1305.65220) Full Text: DOI arXiv